Model Multiplication with Place Value Disks
This Grade 4 Eureka Math skill teaches students to model multiplication using place value disks arranged in equal groups. The key relationship is a times (b times unit) equals (a times b) times unit. For example, to model 3 times 20, students create 3 groups of 2 ten-disks, giving 6 ten-disks with a total value of 60. Similarly, 4 times 300 uses 4 groups of 3 hundred-disks to make 12 hundred-disks, or 1,200. This concrete model from Chapter 10 of Eureka Math Grade 4 builds intuition for multiplying by multiples of 10, 100, and 1,000.
Key Concepts
Multiplying a single digit by a multiple of a place value unit can be modeled by creating equal groups of place value disks. This relationship can be expressed as: $$a \times (b \times \text{unit}) = (a \times b) \times \text{unit}$$.
Common Questions
How do place value disks model multiplication?
Create equal groups of disks, where each disk represents a specific place value unit. The total number of disks times the unit value gives the product.
How do you model 3 times 20 with place value disks?
Create 3 groups of 2 ten-disks. You have 6 ten-disks total. Since each ten-disk equals 10, the product is 6 times 10 = 60.
How do you model 4 times 300 with place value disks?
Create 4 groups of 3 hundred-disks. You have 12 hundred-disks total. Since each equals 100, the product is 12 times 100 = 1,200.
What is the formula for multiplying with place value units?
a times (b times unit) = (a times b) times unit. For example, 3 times (2 tens) = (3 times 2) tens = 6 tens = 60.
How does this model relate to multiplying by 10, 100, or 1,000?
Multiplying by a multiple of a place value shifts all digits up by the corresponding number of places. The disk model makes this shift concrete and visible.